Yep, I can really feel for you!!!!!
But, looking at it..... kids (especially pre-teens and teens) are just known for this kind of thing. Some are masterful... Kids know how to push the right buttons, and it can come with the territory.
I know it is hard, I know how it feels... Yep, it kind of sucks to see my preteen son suck up to others, and not always show the respect and love that I think he should to ME.... After all, I am the 'mom', the 'heavy'... and that's just the way it is.
But, I know that the advice you are getting here is correct.
You need to not take it so personally.
Hide your buttons.
And, while we all know that great mom's are pretty darned devoted to their families... You can't go around 'showing' that to your kids too much.
I agree that you need to 'step back', and regroup the family dynamics...
Everyone should treat everyone with some basic respect...
General, Basic, End of story....
How about the girls Father???
Anyhow,
Disengage with your DD.
(ie. She says "I HATE you...." You in reply... "Yes, that's nice dear..."
You have 'engaged'.
She is pushing your buttons, emotionally....
She is doing what she knows to do as 'winning'.
But, really there are no winners.
Good Luck!!!!
Just know that there a gazillion parents of teens/preteens who are going thru the same thing.... Probably been going on since the beginning of time!